Weighted graphs with Bakry-Emery lower curvature bound K and d-th nonzero eigenvalue near K are forced to be close to a d-dimensional hypercube.
Volume doubling, Poincar´ e inequality and Gaussian heat kernel esti- mate for non-negatively curved graphs
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Quantitative Obata's theorem in discrete setting
Weighted graphs with Bakry-Emery lower curvature bound K and d-th nonzero eigenvalue near K are forced to be close to a d-dimensional hypercube.